Migrated from Lutece 1165 Problem 300 in TCO Round 2A(Changed Version)

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Description

Moose Mod has just learned about the mod operator.Given two positive integers x and y, the mod operator returns the remainder when x is divided by y.For example, 17 mod 5 = 2 because 17 = 3*5 + 2.

Moose Mod has just defined a function that applies a sequence of N mod operators to its input. Formally, the function looks as follows: f(x) = (((x mod m[0]) mod m[1]) ... mod m[N-1]). For example, m = { 10, 3 } corresponds to the function f(x) = (x mod 10) mod 3. For this function we have f(18) = (18 mod 10) mod 3 = 8 mod 3 = 2.

You are given $m$ integers.You are also given a int $R$.Moose Mod is interested in finding the sum f(1) + f(2) + ... + f(R).Compute and output its value.

Input

The first line of the input contains two integers $m(1\leq m\leq5000)$ and $R(1\leq R\leq10^9)$,$R$ means the integer describe above and $m$ means the number of mods.

The second line of the input contains $m$ integers.The ith integer $mod_i$ means the ith mod.$(1\leq mod_i\leq 10^9)$

Output

Print the answer in a single line

Samples

3 10
5 3 2

4

Resources

2015 UESTC ACM Training for Math